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  Gravitational radiation and the validity of the far-zone quadrupole formula in the Newtonian limit of general relativity

Futamase, T., & Schutz, B. F. (1985). Gravitational radiation and the validity of the far-zone quadrupole formula in the Newtonian limit of general relativity. Physical Review D, 32(10), 2557-2565. doi:10.1103/PhysRevD.32.2557.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-7427-3 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-742A-E
Genre: Journal Article

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Futamase, Toshifumi1, 2, Author
Schutz, Bernard F.1, 3, Author              
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1External Organizations, Department of Applied Mathematics and Astronomy, University College, Cardiff, United Kingdom , escidoc:persistent22              
2Max-Planck Institut für Physik und Astrophyisk, Garching bei München, Germany , escidoc:persistent22              
3Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, escidoc:24013              

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 Abstract: We examine the gravitational radiation emitted by a sequence of spacetimes whose near-zone Newtonian limit we have previously studied. The spacetimes are defined by initial data which scale in a Newtonian fashion: the density as ε2, velocity as ε, pressure as ε4, where ε is the sequence parameter. We asymptotically approximate the metric at an event which, as ε→0, remains a fixed number of gravitational wavelengths distant from the system and a fixed number of wave periods to the future of the initial hypersurface. We show that the radiation behaves like that of linearized theory in a Minkowski spacetime, since the mass of the metric vanishes as ε→0. We call this Minkowskian far-zone limiting manifold FM; it is a boundary of the sequence of spacetimes, in which the radiation carries an energy flux given asymptotically by the usual far-zone quadrupole formula (the Landau-Lifshitz formula), as measured both by the Isaacson average stress-energy tensor in FM or by the Bondi flux on IFM+. This proves that the quadrupole formula is an asymptotic approximation to general relativity. We study the relation between Iε+, the sequence of null infinities of the individual manifolds, and IFM+; and we examine the gauge-invariance of FM under certain gauge transformations. We also discuss the relation of this calculation with similar ones in the frame-work of matched asymptotic expansions and others based on the characteristic initial-value problem.

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 Dates: 1985-11-15
 Publication Status: Published in print
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Title: Physical Review D
Source Genre: Journal
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Pages: - Volume / Issue: 32 (10) Sequence Number: - Start / End Page: 2557 - 2565 Identifier: ISSN: 0556-2821